Unless he is compromised in any manner I say turn him out. Most healthy horses dont mind running amuck in the "muck" (meaning mud and rain not manure type muck).
Jolly balls witht he treat hangers on them, Busy Balls, partially deflated basket or soccer balls, 2 liter bottle with pebbles in them and a who plethera of stuff. Also you can feed hay through a hay net or slow feed net to lengthen time spent muching hay. Open a window (if available), work on ground manners like stepping towards you or away from you using hand pressure on certain body parts, picking up feet without touching them or voice commands, Dropping head on command or playing with ears, teaching them how to back up, lead or turn them (pivot) with out a lead rope or lead rope pressure. You can do alot of this in the barn isle way. Unless he has health issues, turn him out, even if its for just an hour; even if its just in the arena (if you have access to one).
"The question is not, can they reason? nor, can they talk? but, can they suffer?" Jeremy Bentham